Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3024,2,Mod(2305,3024)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3024, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3024.2305");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3024.q (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(24.1467615712\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 504) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 2881.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3024.2881 |
Dual form | 3024.2.q.c.2305.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3024\mathbb{Z}\right)^\times\).
\(n\) | \(757\) | \(785\) | \(1135\) | \(2593\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.500000 | + | 0.866025i | −0.223607 | + | 0.387298i | −0.955901 | − | 0.293691i | \(-0.905116\pi\) |
0.732294 | + | 0.680989i | \(0.238450\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.00000 | − | 1.73205i | 0.755929 | − | 0.654654i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.50000 | − | 2.59808i | −0.452267 | − | 0.783349i | 0.546259 | − | 0.837616i | \(-0.316051\pi\) |
−0.998526 | + | 0.0542666i | \(0.982718\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.50000 | − | 2.59808i | −0.416025 | − | 0.720577i | 0.579510 | − | 0.814965i | \(-0.303244\pi\) |
−0.995535 | + | 0.0943882i | \(0.969911\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.50000 | + | 4.33013i | −0.606339 | + | 1.05021i | 0.385499 | + | 0.922708i | \(0.374029\pi\) |
−0.991838 | + | 0.127502i | \(0.959304\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.50000 | + | 6.06218i | 0.802955 | + | 1.39076i | 0.917663 | + | 0.397360i | \(0.130073\pi\) |
−0.114708 | + | 0.993399i | \(0.536593\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.50000 | + | 4.33013i | −0.521286 | + | 0.902894i | 0.478407 | + | 0.878138i | \(0.341214\pi\) |
−0.999694 | + | 0.0247559i | \(0.992119\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.00000 | + | 3.46410i | 0.400000 | + | 0.692820i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.500000 | + | 0.866025i | −0.0928477 | + | 0.160817i | −0.908708 | − | 0.417432i | \(-0.862930\pi\) |
0.815861 | + | 0.578249i | \(0.196264\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.00000 | 1.43684 | 0.718421 | − | 0.695608i | \(-0.244865\pi\) | ||||
0.718421 | + | 0.695608i | \(0.244865\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.500000 | + | 2.59808i | 0.0845154 | + | 0.439155i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.50000 | − | 2.59808i | −0.246598 | − | 0.427121i | 0.715981 | − | 0.698119i | \(-0.245980\pi\) |
−0.962580 | + | 0.270998i | \(0.912646\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.50000 | − | 4.33013i | −0.390434 | − | 0.676252i | 0.602072 | − | 0.798441i | \(-0.294342\pi\) |
−0.992507 | + | 0.122189i | \(0.961009\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.50000 | + | 6.06218i | −0.533745 | + | 0.924473i | 0.465478 | + | 0.885059i | \(0.345882\pi\) |
−0.999223 | + | 0.0394140i | \(0.987451\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 8.00000 | 1.16692 | 0.583460 | − | 0.812142i | \(-0.301699\pi\) | ||||
0.583460 | + | 0.812142i | \(0.301699\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | − | 6.92820i | 0.142857 | − | 0.989743i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.500000 | + | 0.866025i | −0.0686803 | + | 0.118958i | −0.898321 | − | 0.439340i | \(-0.855212\pi\) |
0.829640 | + | 0.558298i | \(0.188546\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.00000 | 0.404520 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.0000 | 1.28037 | 0.640184 | − | 0.768221i | \(-0.278858\pi\) | ||||
0.640184 | + | 0.768221i | \(0.278858\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.00000 | 0.372104 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 12.0000 | 1.46603 | 0.733017 | − | 0.680211i | \(-0.238112\pi\) | ||||
0.733017 | + | 0.680211i | \(0.238112\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12.0000 | 1.42414 | 0.712069 | − | 0.702109i | \(-0.247758\pi\) | ||||
0.712069 | + | 0.702109i | \(0.247758\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.50000 | − | 4.33013i | 0.292603 | − | 0.506803i | −0.681822 | − | 0.731519i | \(-0.738812\pi\) |
0.974424 | + | 0.224716i | \(0.0721453\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −7.50000 | − | 2.59808i | −0.854704 | − | 0.296078i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.00000 | 0.900070 | 0.450035 | − | 0.893011i | \(-0.351411\pi\) | ||||
0.450035 | + | 0.893011i | \(0.351411\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 7.50000 | − | 12.9904i | 0.823232 | − | 1.42588i | −0.0800311 | − | 0.996792i | \(-0.525502\pi\) |
0.903263 | − | 0.429087i | \(-0.141165\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.50000 | − | 4.33013i | −0.271163 | − | 0.469668i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.50000 | − | 4.33013i | −0.264999 | − | 0.458993i | 0.702564 | − | 0.711621i | \(-0.252038\pi\) |
−0.967563 | + | 0.252628i | \(0.918705\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −7.50000 | − | 2.59808i | −0.786214 | − | 0.272352i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −7.00000 | −0.718185 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.50000 | + | 6.06218i | −0.355371 | + | 0.615521i | −0.987181 | − | 0.159602i | \(-0.948979\pi\) |
0.631810 | + | 0.775123i | \(0.282312\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.50000 | − | 7.79423i | −0.447767 | − | 0.775555i | 0.550474 | − | 0.834853i | \(-0.314447\pi\) |
−0.998240 | + | 0.0592978i | \(0.981114\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −7.50000 | + | 12.9904i | −0.738997 | + | 1.27998i | 0.213950 | + | 0.976845i | \(0.431367\pi\) |
−0.952947 | + | 0.303136i | \(0.901966\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 4.50000 | + | 7.79423i | 0.435031 | + | 0.753497i | 0.997298 | − | 0.0734594i | \(-0.0234039\pi\) |
−0.562267 | + | 0.826956i | \(0.690071\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.50000 | + | 6.06218i | −0.335239 | + | 0.580651i | −0.983531 | − | 0.180741i | \(-0.942150\pi\) |
0.648292 | + | 0.761392i | \(0.275484\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 7.50000 | + | 12.9904i | 0.705541 | + | 1.22203i | 0.966496 | + | 0.256681i | \(0.0826291\pi\) |
−0.260955 | + | 0.965351i | \(0.584038\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.50000 | − | 4.33013i | −0.233126 | − | 0.403786i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.50000 | + | 12.9904i | 0.229175 | + | 1.19083i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | − | 1.73205i | 0.0909091 | − | 0.157459i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −9.00000 | −0.804984 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.00000 | 0.354943 | 0.177471 | − | 0.984126i | \(-0.443208\pi\) | ||||
0.177471 | + | 0.984126i | \(0.443208\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.50000 | − | 6.06218i | 0.305796 | − | 0.529655i | −0.671642 | − | 0.740876i | \(-0.734411\pi\) |
0.977438 | + | 0.211221i | \(0.0677440\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 17.5000 | + | 6.06218i | 1.51744 | + | 0.525657i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 11.5000 | + | 19.9186i | 0.982511 | + | 1.70176i | 0.652512 | + | 0.757778i | \(0.273715\pi\) |
0.329999 | + | 0.943981i | \(0.392952\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.50000 | − | 7.79423i | −0.381685 | − | 0.661098i | 0.609618 | − | 0.792695i | \(-0.291323\pi\) |
−0.991303 | + | 0.131597i | \(0.957989\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −4.50000 | + | 7.79423i | −0.376309 | + | 0.651786i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.500000 | − | 0.866025i | −0.0415227 | − | 0.0719195i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2.50000 | + | 4.33013i | −0.204808 | + | 0.354738i | −0.950072 | − | 0.312032i | \(-0.898990\pi\) |
0.745264 | + | 0.666770i | \(0.232324\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.50000 | − | 4.33013i | −0.203447 | − | 0.352381i | 0.746190 | − | 0.665733i | \(-0.231881\pi\) |
−0.949637 | + | 0.313353i | \(0.898548\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4.00000 | + | 6.92820i | −0.321288 | + | 0.556487i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.00000 | −0.478852 | −0.239426 | − | 0.970915i | \(-0.576959\pi\) | ||||
−0.239426 | + | 0.970915i | \(0.576959\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.50000 | + | 12.9904i | 0.197028 | + | 1.02379i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.50000 | − | 4.33013i | −0.195815 | − | 0.339162i | 0.751352 | − | 0.659901i | \(-0.229402\pi\) |
−0.947167 | + | 0.320740i | \(0.896069\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 10.5000 | + | 18.1865i | 0.812514 | + | 1.40732i | 0.911099 | + | 0.412188i | \(0.135235\pi\) |
−0.0985846 | + | 0.995129i | \(0.531432\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.00000 | − | 3.46410i | 0.153846 | − | 0.266469i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2.00000 | −0.152057 | −0.0760286 | − | 0.997106i | \(-0.524224\pi\) | ||||
−0.0760286 | + | 0.997106i | \(0.524224\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 10.0000 | + | 3.46410i | 0.755929 | + | 0.261861i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2.50000 | + | 4.33013i | −0.186859 | + | 0.323649i | −0.944201 | − | 0.329369i | \(-0.893164\pi\) |
0.757343 | + | 0.653018i | \(0.226497\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.00000 | 0.148659 | 0.0743294 | − | 0.997234i | \(-0.476318\pi\) | ||||
0.0743294 | + | 0.997234i | \(0.476318\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3.00000 | 0.220564 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 15.0000 | 1.09691 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 16.0000 | 1.15772 | 0.578860 | − | 0.815427i | \(-0.303498\pi\) | ||||
0.578860 | + | 0.815427i | \(0.303498\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −18.0000 | −1.29567 | −0.647834 | − | 0.761781i | \(-0.724325\pi\) | ||||
−0.647834 | + | 0.761781i | \(0.724325\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 6.00000 | 0.427482 | 0.213741 | − | 0.976890i | \(-0.431435\pi\) | ||||
0.213741 | + | 0.976890i | \(0.431435\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −9.50000 | + | 16.4545i | −0.673437 | + | 1.16643i | 0.303486 | + | 0.952836i | \(0.401849\pi\) |
−0.976923 | + | 0.213591i | \(0.931484\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.500000 | + | 2.59808i | 0.0350931 | + | 0.182349i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.00000 | 0.349215 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 10.5000 | − | 18.1865i | 0.726300 | − | 1.25799i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.50000 | − | 11.2583i | −0.447478 | − | 0.775055i | 0.550743 | − | 0.834675i | \(-0.314345\pi\) |
−0.998221 | + | 0.0596196i | \(0.981011\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −3.50000 | − | 6.06218i | −0.238698 | − | 0.413437i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 16.0000 | − | 13.8564i | 1.08615 | − | 0.940634i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 15.0000 | 1.00901 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 10.5000 | − | 18.1865i | 0.703132 | − | 1.21786i | −0.264229 | − | 0.964460i | \(-0.585118\pi\) |
0.967361 | − | 0.253401i | \(-0.0815490\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −5.50000 | − | 9.52628i | −0.365048 | − | 0.632281i | 0.623736 | − | 0.781635i | \(-0.285614\pi\) |
−0.988784 | + | 0.149354i | \(0.952281\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0.500000 | − | 0.866025i | 0.0330409 | − | 0.0572286i | −0.849032 | − | 0.528341i | \(-0.822814\pi\) |
0.882073 | + | 0.471113i | \(0.156147\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 5.50000 | + | 9.52628i | 0.360317 | + | 0.624087i | 0.988013 | − | 0.154371i | \(-0.0493352\pi\) |
−0.627696 | + | 0.778459i | \(0.716002\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.00000 | + | 6.92820i | −0.260931 | + | 0.451946i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 12.5000 | + | 21.6506i | 0.808558 | + | 1.40046i | 0.913863 | + | 0.406023i | \(0.133085\pi\) |
−0.105305 | + | 0.994440i | \(0.533582\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.50000 | + | 4.33013i | 0.161039 | + | 0.278928i | 0.935242 | − | 0.354010i | \(-0.115182\pi\) |
−0.774202 | + | 0.632938i | \(0.781849\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 5.50000 | + | 4.33013i | 0.351382 | + | 0.276642i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 10.5000 | − | 18.1865i | 0.668099 | − | 1.15718i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −20.0000 | −1.26239 | −0.631194 | − | 0.775625i | \(-0.717435\pi\) | ||||
−0.631194 | + | 0.775625i | \(0.717435\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 15.0000 | 0.943042 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −10.5000 | + | 18.1865i | −0.654972 | + | 1.13444i | 0.326929 | + | 0.945049i | \(0.393986\pi\) |
−0.981901 | + | 0.189396i | \(0.939347\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −7.50000 | − | 2.59808i | −0.466027 | − | 0.161437i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −13.5000 | − | 23.3827i | −0.832446 | − | 1.44184i | −0.896093 | − | 0.443866i | \(-0.853607\pi\) |
0.0636476 | − | 0.997972i | \(-0.479727\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.500000 | − | 0.866025i | −0.0307148 | − | 0.0531995i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.50000 | − | 2.59808i | 0.0914566 | − | 0.158408i | −0.816668 | − | 0.577108i | \(-0.804181\pi\) |
0.908124 | + | 0.418701i | \(0.137514\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 11.5000 | + | 19.9186i | 0.698575 | + | 1.20997i | 0.968960 | + | 0.247216i | \(0.0795156\pi\) |
−0.270385 | + | 0.962752i | \(0.587151\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 6.00000 | − | 10.3923i | 0.361814 | − | 0.626680i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.50000 | + | 4.33013i | 0.150210 | + | 0.260172i | 0.931305 | − | 0.364241i | \(-0.118672\pi\) |
−0.781094 | + | 0.624413i | \(0.785338\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 13.5000 | − | 23.3827i | 0.805342 | − | 1.39489i | −0.110717 | − | 0.993852i | \(-0.535315\pi\) |
0.916060 | − | 0.401042i | \(-0.131352\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.00000 | 0.237775 | 0.118888 | − | 0.992908i | \(-0.462067\pi\) | ||||
0.118888 | + | 0.992908i | \(0.462067\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −12.5000 | − | 4.33013i | −0.737852 | − | 0.255599i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4.00000 | − | 6.92820i | −0.235294 | − | 0.407541i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 13.5000 | + | 23.3827i | 0.788678 | + | 1.36603i | 0.926777 | + | 0.375613i | \(0.122568\pi\) |
−0.138098 | + | 0.990419i | \(0.544099\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 15.0000 | 0.867472 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.50000 | + | 18.1865i | 0.201737 | + | 1.04825i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −5.00000 | + | 8.66025i | −0.286299 | + | 0.495885i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4.00000 | −0.228292 | −0.114146 | − | 0.993464i | \(-0.536413\pi\) | ||||
−0.114146 | + | 0.993464i | \(0.536413\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −34.0000 | −1.92179 | −0.960897 | − | 0.276907i | \(-0.910691\pi\) | ||||
−0.960897 | + | 0.276907i | \(0.910691\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 30.0000 | 1.68497 | 0.842484 | − | 0.538721i | \(-0.181092\pi\) | ||||
0.842484 | + | 0.538721i | \(0.181092\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.00000 | 0.167968 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −35.0000 | −1.94745 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6.00000 | − | 10.3923i | 0.332820 | − | 0.576461i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 16.0000 | − | 13.8564i | 0.882109 | − | 0.763928i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.00000 | −0.439720 | −0.219860 | − | 0.975531i | \(-0.570560\pi\) | ||||
−0.219860 | + | 0.975531i | \(0.570560\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −6.00000 | + | 10.3923i | −0.327815 | + | 0.567792i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6.50000 | + | 11.2583i | 0.354078 | + | 0.613280i | 0.986960 | − | 0.160968i | \(-0.0514616\pi\) |
−0.632882 | + | 0.774248i | \(0.718128\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −12.0000 | − | 20.7846i | −0.649836 | − | 1.12555i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −10.0000 | − | 15.5885i | −0.539949 | − | 0.841698i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −12.0000 | −0.644194 | −0.322097 | − | 0.946707i | \(-0.604388\pi\) | ||||
−0.322097 | + | 0.946707i | \(0.604388\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −5.50000 | + | 9.52628i | −0.294408 | + | 0.509930i | −0.974847 | − | 0.222875i | \(-0.928456\pi\) |
0.680439 | + | 0.732805i | \(0.261789\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −10.5000 | − | 18.1865i | −0.558859 | − | 0.967972i | −0.997592 | − | 0.0693543i | \(-0.977906\pi\) |
0.438733 | − | 0.898617i | \(-0.355427\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6.00000 | + | 10.3923i | −0.318447 | + | 0.551566i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1.50000 | − | 2.59808i | −0.0791670 | − | 0.137121i | 0.823724 | − | 0.566991i | \(-0.191893\pi\) |
−0.902891 | + | 0.429870i | \(0.858559\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.0000 | + | 25.9808i | −0.789474 | + | 1.36741i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.50000 | + | 4.33013i | 0.130856 | + | 0.226649i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6.50000 | − | 11.2583i | −0.339297 | − | 0.587680i | 0.645003 | − | 0.764180i | \(-0.276856\pi\) |
−0.984301 | + | 0.176500i | \(0.943523\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.500000 | + | 2.59808i | 0.0259587 | + | 0.134885i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0.500000 | − | 0.866025i | 0.0258890 | − | 0.0448411i | −0.852791 | − | 0.522253i | \(-0.825092\pi\) |
0.878680 | + | 0.477412i | \(0.158425\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3.00000 | 0.154508 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −36.0000 | −1.84920 | −0.924598 | − | 0.380945i | \(-0.875599\pi\) | ||||
−0.924598 | + | 0.380945i | \(0.875599\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.50000 | − | 2.59808i | 0.0766464 | − | 0.132755i | −0.825155 | − | 0.564907i | \(-0.808912\pi\) |
0.901801 | + | 0.432151i | \(0.142245\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 6.00000 | − | 5.19615i | 0.305788 | − | 0.264820i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −8.50000 | − | 14.7224i | −0.430967 | − | 0.746457i | 0.565990 | − | 0.824412i | \(-0.308494\pi\) |
−0.996957 | + | 0.0779554i | \(0.975161\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −12.5000 | − | 21.6506i | −0.632152 | − | 1.09492i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −4.00000 | + | 6.92820i | −0.201262 | + | 0.348596i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 8.50000 | + | 14.7224i | 0.426603 | + | 0.738898i | 0.996569 | − | 0.0827707i | \(-0.0263769\pi\) |
−0.569966 | + | 0.821668i | \(0.693044\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.50000 | − | 2.59808i | 0.0749064 | − | 0.129742i | −0.826139 | − | 0.563466i | \(-0.809468\pi\) |
0.901046 | + | 0.433724i | \(0.142801\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −12.0000 | − | 20.7846i | −0.597763 | − | 1.03536i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4.50000 | + | 7.79423i | −0.223057 | + | 0.386346i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 6.00000 | 0.296681 | 0.148340 | − | 0.988936i | \(-0.452607\pi\) | ||||
0.148340 | + | 0.988936i | \(0.452607\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 7.50000 | + | 12.9904i | 0.368161 | + | 0.637673i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −11.5000 | − | 19.9186i | −0.561812 | − | 0.973087i | −0.997338 | − | 0.0729107i | \(-0.976771\pi\) |
0.435527 | − | 0.900176i | \(-0.356562\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.50000 | + | 6.06218i | −0.170580 | + | 0.295452i | −0.938623 | − | 0.344946i | \(-0.887897\pi\) |
0.768043 | + | 0.640398i | \(0.221231\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −20.0000 | −0.970143 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 20.0000 | − | 17.3205i | 0.967868 | − | 0.838198i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 7.50000 | − | 12.9904i | 0.361262 | − | 0.625725i | −0.626907 | − | 0.779094i | \(-0.715679\pi\) |
0.988169 | + | 0.153370i | \(0.0490126\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −14.0000 | −0.672797 | −0.336399 | − | 0.941720i | \(-0.609209\pi\) | ||||
−0.336399 | + | 0.941720i | \(0.609209\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −35.0000 | −1.67428 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 20.0000 | 0.950229 | 0.475114 | − | 0.879924i | \(-0.342407\pi\) | ||||
0.475114 | + | 0.879924i | \(0.342407\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 5.00000 | 0.237023 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −22.0000 | −1.03824 | −0.519122 | − | 0.854700i | \(-0.673741\pi\) | ||||
−0.519122 | + | 0.854700i | \(0.673741\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −7.50000 | + | 12.9904i | −0.353161 | + | 0.611693i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 6.00000 | − | 5.19615i | 0.281284 | − | 0.243599i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 22.0000 | 1.02912 | 0.514558 | − | 0.857455i | \(-0.327956\pi\) | ||||
0.514558 | + | 0.857455i | \(0.327956\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −10.5000 | + | 18.1865i | −0.489034 | + | 0.847031i | −0.999920 | − | 0.0126168i | \(-0.995984\pi\) |
0.510887 | + | 0.859648i | \(0.329317\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 17.5000 | + | 30.3109i | 0.813294 | + | 1.40867i | 0.910546 | + | 0.413407i | \(0.135661\pi\) |
−0.0972525 | + | 0.995260i | \(0.531005\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −13.5000 | − | 23.3827i | −0.624705 | − | 1.08202i | −0.988598 | − | 0.150581i | \(-0.951886\pi\) |
0.363892 | − | 0.931441i | \(-0.381448\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 24.0000 | − | 20.7846i | 1.10822 | − | 0.959744i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 21.0000 | 0.965581 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −14.0000 | + | 24.2487i | −0.642364 | + | 1.11261i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −3.50000 | − | 6.06218i | −0.159919 | − | 0.276988i | 0.774920 | − | 0.632059i | \(-0.217790\pi\) |
−0.934839 | + | 0.355071i | \(0.884457\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.50000 | + | 7.79423i | −0.205182 | + | 0.355386i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −3.50000 | − | 6.06218i | −0.158927 | − | 0.275269i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 18.5000 | − | 32.0429i | 0.838315 | − | 1.45200i | −0.0529875 | − | 0.998595i | \(-0.516874\pi\) |
0.891303 | − | 0.453409i | \(-0.149792\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 10.5000 | + | 18.1865i | 0.473858 | + | 0.820747i | 0.999552 | − | 0.0299272i | \(-0.00952753\pi\) |
−0.525694 | + | 0.850674i | \(0.676194\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.50000 | − | 4.33013i | −0.112594 | − | 0.195019i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 24.0000 | − | 20.7846i | 1.07655 | − | 0.932317i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0.500000 | − | 0.866025i | 0.0223831 | − | 0.0387686i | −0.854617 | − | 0.519259i | \(-0.826208\pi\) |
0.877000 | + | 0.480490i | \(0.159541\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 40.0000 | 1.78351 | 0.891756 | − | 0.452517i | \(-0.149474\pi\) | ||||
0.891756 | + | 0.452517i | \(0.149474\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 9.00000 | 0.400495 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −10.5000 | + | 18.1865i | −0.465404 | + | 0.806104i | −0.999220 | − | 0.0394971i | \(-0.987424\pi\) |
0.533815 | + | 0.845601i | \(0.320758\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.50000 | − | 12.9904i | −0.110593 | − | 0.574661i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −7.50000 | − | 12.9904i | −0.330489 | − | 0.572425i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −12.0000 | − | 20.7846i | −0.527759 | − | 0.914106i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.50000 | − | 2.59808i | 0.0657162 | − | 0.113824i | −0.831295 | − | 0.555831i | \(-0.812400\pi\) |
0.897011 | + | 0.442007i | \(0.145733\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −12.5000 | − | 21.6506i | −0.546587 | − | 0.946716i | −0.998505 | − | 0.0546569i | \(-0.982594\pi\) |
0.451918 | − | 0.892059i | \(-0.350740\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −20.0000 | + | 34.6410i | −0.871214 | + | 1.50899i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.00000 | − | 1.73205i | −0.0434783 | − | 0.0753066i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −7.50000 | + | 12.9904i | −0.324861 | + | 0.562676i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −9.00000 | −0.389104 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −19.5000 | + | 7.79423i | −0.839924 | + | 0.335721i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −15.5000 | − | 26.8468i | −0.666397 | − | 1.15423i | −0.978905 | − | 0.204318i | \(-0.934502\pi\) |
0.312507 | − | 0.949915i | \(-0.398831\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −3.50000 | − | 6.06218i | −0.149924 | − | 0.259675i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −17.5000 | + | 30.3109i | −0.748246 | + | 1.29600i | 0.200417 | + | 0.979711i | \(0.435770\pi\) |
−0.948663 | + | 0.316289i | \(0.897563\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −7.00000 | −0.298210 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 16.0000 | − | 13.8564i | 0.680389 | − | 0.589234i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 9.50000 | − | 16.4545i | 0.402528 | − | 0.697199i | −0.591502 | − | 0.806303i | \(-0.701465\pi\) |
0.994030 | + | 0.109104i | \(0.0347983\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 21.0000 | 0.888205 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 4.00000 | 0.168580 | 0.0842900 | − | 0.996441i | \(-0.473138\pi\) | ||||
0.0842900 | + | 0.996441i | \(0.473138\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −15.0000 | −0.631055 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −30.0000 | −1.25767 | −0.628833 | − | 0.777541i | \(-0.716467\pi\) | ||||
−0.628833 | + | 0.777541i | \(0.716467\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −32.0000 | −1.33916 | −0.669579 | − | 0.742741i | \(-0.733526\pi\) | ||||
−0.669579 | + | 0.742741i | \(0.733526\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −20.0000 | −0.834058 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4.50000 | − | 7.79423i | 0.187337 | − | 0.324478i | −0.757024 | − | 0.653387i | \(-0.773348\pi\) |
0.944362 | + | 0.328909i | \(0.106681\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −7.50000 | − | 38.9711i | −0.311152 | − | 1.61680i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.00000 | 0.124247 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 17.5000 | − | 30.3109i | 0.722302 | − | 1.25106i | −0.237773 | − | 0.971321i | \(-0.576417\pi\) |
0.960075 | − | 0.279743i | \(-0.0902494\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 28.0000 | + | 48.4974i | 1.15372 | + | 1.99830i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −16.5000 | − | 28.5788i | −0.677574 | − | 1.17359i | −0.975709 | − | 0.219069i | \(-0.929698\pi\) |
0.298136 | − | 0.954524i | \(-0.403635\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −12.5000 | − | 4.33013i | −0.512450 | − | 0.177518i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 16.0000 | 0.653742 | 0.326871 | − | 0.945069i | \(-0.394006\pi\) | ||||
0.326871 | + | 0.945069i | \(0.394006\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −3.50000 | + | 6.06218i | −0.142768 | + | 0.247281i | −0.928538 | − | 0.371237i | \(-0.878934\pi\) |
0.785770 | + | 0.618519i | \(0.212267\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.00000 | + | 1.73205i | 0.0406558 | + | 0.0704179i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −11.5000 | + | 19.9186i | −0.466771 | + | 0.808470i | −0.999279 | − | 0.0379540i | \(-0.987916\pi\) |
0.532509 | + | 0.846424i | \(0.321249\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −12.0000 | − | 20.7846i | −0.485468 | − | 0.840855i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −21.5000 | + | 37.2391i | −0.868377 | + | 1.50407i | −0.00472215 | + | 0.999989i | \(0.501503\pi\) |
−0.863655 | + | 0.504084i | \(0.831830\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 13.5000 | + | 23.3827i | 0.543490 | + | 0.941351i | 0.998700 | + | 0.0509678i | \(0.0162306\pi\) |
−0.455211 | + | 0.890384i | \(0.650436\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 7.50000 | + | 12.9904i | 0.301450 | + | 0.522127i | 0.976465 | − | 0.215677i | \(-0.0691959\pi\) |
−0.675014 | + | 0.737805i | \(0.735863\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −12.5000 | − | 4.33013i | −0.500802 | − | 0.173483i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −5.50000 | + | 9.52628i | −0.220000 | + | 0.381051i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 15.0000 | 0.598089 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 40.0000 | 1.59237 | 0.796187 | − | 0.605050i | \(-0.206847\pi\) | ||||
0.796187 | + | 0.605050i | \(0.206847\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −2.00000 | + | 3.46410i | −0.0793676 | + | 0.137469i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −19.5000 | + | 7.79423i | −0.772618 | + | 0.308819i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −8.50000 | − | 14.7224i | −0.335730 | − | 0.581501i | 0.647895 | − | 0.761730i | \(-0.275650\pi\) |
−0.983625 | + | 0.180229i | \(0.942316\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 21.5000 | + | 37.2391i | 0.847877 | + | 1.46857i | 0.883099 | + | 0.469187i | \(0.155453\pi\) |
−0.0352216 | + | 0.999380i | \(0.511214\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −4.50000 | + | 7.79423i | −0.176913 | + | 0.306423i | −0.940822 | − | 0.338902i | \(-0.889945\pi\) |
0.763908 | + | 0.645325i | \(0.223278\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −6.50000 | + | 11.2583i | −0.254365 | + | 0.440573i | −0.964723 | − | 0.263268i | \(-0.915200\pi\) |
0.710358 | + | 0.703840i | \(0.248533\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.50000 | + | 6.06218i | 0.136756 | + | 0.236869i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −14.5000 | + | 25.1147i | −0.564840 | + | 0.978331i | 0.432225 | + | 0.901766i | \(0.357729\pi\) |
−0.997065 | + | 0.0765653i | \(0.975605\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −46.0000 | −1.78919 | −0.894596 | − | 0.446875i | \(-0.852537\pi\) | ||||
−0.894596 | + | 0.446875i | \(0.852537\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −14.0000 | + | 12.1244i | −0.542897 | + | 0.470162i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.50000 | − | 4.33013i | −0.0968004 | − | 0.167663i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −15.0000 | − | 25.9808i | −0.579069 | − | 1.00298i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 14.5000 | − | 25.1147i | 0.558934 | − | 0.968102i | −0.438652 | − | 0.898657i | \(-0.644544\pi\) |
0.997586 | − | 0.0694449i | \(-0.0221228\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −18.0000 | −0.691796 | −0.345898 | − | 0.938272i | \(-0.612426\pi\) | ||||
−0.345898 | + | 0.938272i | \(0.612426\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.50000 | + | 18.1865i | 0.134318 | + | 0.697935i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 19.5000 | − | 33.7750i | 0.746147 | − | 1.29236i | −0.203510 | − | 0.979073i | \(-0.565235\pi\) |
0.949657 | − | 0.313291i | \(-0.101432\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −23.0000 | −0.878785 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 3.00000 | 0.114291 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 28.0000 | 1.06517 | 0.532585 | − | 0.846376i | \(-0.321221\pi\) | ||||
0.532585 | + | 0.846376i | \(0.321221\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 9.00000 | 0.341389 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 25.0000 | 0.946943 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2.00000 | 0.0755390 | 0.0377695 | − | 0.999286i | \(-0.487975\pi\) | ||||
0.0377695 | + | 0.999286i | \(0.487975\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 10.5000 | − | 18.1865i | 0.396015 | − | 0.685918i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −22.5000 | − | 7.79423i | −0.846200 | − | 0.293132i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −38.0000 | −1.42712 | −0.713560 | − | 0.700594i | \(-0.752918\pi\) | ||||
−0.713560 | + | 0.700594i | \(0.752918\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −20.0000 | + | 34.6410i | −0.749006 | + | 1.29732i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4.50000 | − | 7.79423i | −0.168290 | − | 0.291488i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 10.5000 | + | 18.1865i | 0.391584 | + | 0.678243i | 0.992659 | − | 0.120950i | \(-0.0385939\pi\) |
−0.601075 | + | 0.799193i | \(0.705261\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 7.50000 | + | 38.9711i | 0.279315 | + | 1.45136i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −4.00000 | −0.148556 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −3.50000 | + | 6.06218i | −0.129808 | + | 0.224834i | −0.923602 | − | 0.383353i | \(-0.874769\pi\) |
0.793794 | + | 0.608186i | \(0.208103\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −17.5000 | − | 30.3109i | −0.647261 | − | 1.12109i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 14.5000 | − | 25.1147i | 0.535570 | − | 0.927634i | −0.463566 | − | 0.886062i | \(-0.653430\pi\) |
0.999136 | − | 0.0415715i | \(-0.0132364\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −18.0000 | − | 31.1769i | −0.663039 | − | 1.14842i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 0.500000 | − | 0.866025i | 0.0183928 | − | 0.0318573i | −0.856683 | − | 0.515844i | \(-0.827478\pi\) |
0.875075 | + | 0.483987i | \(0.160812\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 24.5000 | + | 42.4352i | 0.898818 | + | 1.55680i | 0.829007 | + | 0.559238i | \(0.188906\pi\) |
0.0698106 | + | 0.997560i | \(0.477761\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.50000 | − | 4.33013i | −0.0915929 | − | 0.158644i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 22.5000 | + | 7.79423i | 0.822132 | + | 0.284795i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −3.50000 | + | 6.06218i | −0.127717 | + | 0.221212i | −0.922792 | − | 0.385299i | \(-0.874098\pi\) |
0.795075 | + | 0.606511i | \(0.207432\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 5.00000 | 0.181969 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −38.0000 | −1.38113 | −0.690567 | − | 0.723269i | \(-0.742639\pi\) | ||||
−0.690567 | + | 0.723269i | \(0.742639\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 13.5000 | − | 23.3827i | 0.489375 | − | 0.847622i | −0.510551 | − | 0.859848i | \(-0.670558\pi\) |
0.999925 | + | 0.0122260i | \(0.00389175\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3.50000 | + | 18.1865i | 0.126709 | + | 0.658397i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −15.5000 | − | 26.8468i | −0.558944 | − | 0.968120i | −0.997585 | − | 0.0694574i | \(-0.977873\pi\) |
0.438641 | − | 0.898663i | \(-0.355460\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −8.50000 | + | 14.7224i | −0.305724 | + | 0.529529i | −0.977422 | − | 0.211296i | \(-0.932232\pi\) |
0.671698 | + | 0.740825i | \(0.265565\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 16.0000 | + | 27.7128i | 0.574737 | + | 0.995474i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 17.5000 | − | 30.3109i | 0.627003 | − | 1.08600i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −18.0000 | − | 31.1769i | −0.644091 | − | 1.11560i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 3.00000 | − | 5.19615i | 0.107075 | − | 0.185459i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −52.0000 | −1.85360 | −0.926800 | − | 0.375555i | \(-0.877452\pi\) | ||||
−0.926800 | + | 0.375555i | \(0.877452\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 37.5000 | + | 12.9904i | 1.33335 | + | 0.461885i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −15.0000 | − | 25.9808i | −0.532666 | − | 0.922604i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −16.5000 | − | 28.5788i | −0.584460 | − | 1.01231i | −0.994943 | − | 0.100446i | \(-0.967973\pi\) |
0.410483 | − | 0.911868i | \(-0.365360\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −20.0000 | + | 34.6410i | −0.707549 | + | 1.22551i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −15.0000 | −0.529339 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −12.5000 | − | 4.33013i | −0.440567 | − | 0.152617i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −16.5000 | + | 28.5788i | −0.580109 | + | 1.00478i | 0.415357 | + | 0.909659i | \(0.363657\pi\) |
−0.995466 | + | 0.0951198i | \(0.969677\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −12.0000 | −0.421377 | −0.210688 | − | 0.977553i | \(-0.567571\pi\) | ||||
−0.210688 | + | 0.977553i | \(0.567571\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 5.00000 | 0.175142 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −49.0000 | −1.71429 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 42.0000 | 1.46581 | 0.732905 | − | 0.680331i | \(-0.238164\pi\) | ||||
0.732905 | + | 0.680331i | \(0.238164\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −8.00000 | −0.278862 | −0.139431 | − | 0.990232i | \(-0.544527\pi\) | ||||
−0.139431 | + | 0.990232i | \(0.544527\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 36.0000 | 1.25184 | 0.625921 | − | 0.779886i | \(-0.284723\pi\) | ||||
0.625921 | + | 0.779886i | \(0.284723\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 12.5000 | − | 21.6506i | 0.434143 | − | 0.751958i | −0.563082 | − | 0.826401i | \(-0.690385\pi\) |
0.997225 | + | 0.0744432i | \(0.0237179\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 27.5000 | + | 21.6506i | 0.952819 | + | 0.750150i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −21.0000 | −0.726735 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.50000 | − | 2.59808i | 0.0517858 | − | 0.0896956i | −0.838971 | − | 0.544177i | \(-0.816842\pi\) |
0.890756 | + | 0.454481i | \(0.150175\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 14.0000 | + | 24.2487i | 0.482759 | + | 0.836162i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 2.00000 | + | 3.46410i | 0.0688021 | + | 0.119169i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.00000 | − | 5.19615i | −0.0343604 | − | 0.178542i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 15.0000 | 0.514193 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 26.5000 | − | 45.8993i | 0.907343 | − | 1.57156i | 0.0896015 | − | 0.995978i | \(-0.471441\pi\) |
0.817741 | − | 0.575586i | \(-0.195226\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −22.5000 | − | 38.9711i | −0.768585 | − | 1.33123i | −0.938330 | − | 0.345741i | \(-0.887628\pi\) |
0.169745 | − | 0.985488i | \(-0.445706\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −11.5000 | + | 19.9186i | −0.392375 | + | 0.679613i | −0.992762 | − | 0.120096i | \(-0.961680\pi\) |
0.600387 | + | 0.799709i | \(0.295013\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −23.5000 | − | 40.7032i | −0.799949 | − | 1.38555i | −0.919648 | − | 0.392743i | \(-0.871526\pi\) |
0.119699 | − | 0.992810i | \(-0.461807\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.00000 | − | 1.73205i | 0.0340010 | − | 0.0588915i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −12.0000 | − | 20.7846i | −0.407072 | − | 0.705070i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −18.0000 | − | 31.1769i | −0.609907 | − | 1.05639i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −18.0000 | + | 15.5885i | −0.608511 | + | 0.526986i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 18.5000 | − | 32.0429i | 0.624701 | − | 1.08201i | −0.363898 | − | 0.931439i | \(-0.618554\pi\) |
0.988599 | − | 0.150574i | \(-0.0481123\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −22.0000 | −0.741199 | −0.370599 | − | 0.928793i | \(-0.620848\pi\) | ||||
−0.370599 | + | 0.928793i | \(0.620848\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 44.0000 | 1.48072 | 0.740359 | − | 0.672212i | \(-0.234656\pi\) | ||||
0.740359 | + | 0.672212i | \(0.234656\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.50000 | − | 2.59808i | 0.0503651 | − | 0.0872349i | −0.839744 | − | 0.542983i | \(-0.817295\pi\) |
0.890109 | + | 0.455748i | \(0.150628\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 8.00000 | − | 6.92820i | 0.268311 | − | 0.232364i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 28.0000 | + | 48.4974i | 0.936984 | + | 1.62290i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2.50000 | − | 4.33013i | −0.0835658 | − | 0.144740i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −4.00000 | + | 6.92820i | −0.133407 | + | 0.231069i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.50000 | − | 4.33013i | −0.0832871 | − | 0.144257i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1.00000 | + | 1.73205i | −0.0332411 | + | 0.0575753i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −18.5000 | − | 32.0429i | −0.614282 | − | 1.06397i | −0.990510 | − | 0.137441i | \(-0.956112\pi\) |
0.376228 | − | 0.926527i | \(-0.377221\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −6.50000 | + | 11.2583i | −0.215355 | + | 0.373005i | −0.953382 | − | 0.301765i | \(-0.902424\pi\) |
0.738028 | + | 0.674771i | \(0.235757\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −45.0000 | −1.48928 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −3.50000 | − | 18.1865i | −0.115580 | − | 0.600572i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −20.5000 | − | 35.5070i | −0.676233 | − | 1.17127i | −0.976107 | − | 0.217291i | \(-0.930278\pi\) |
0.299874 | − | 0.953979i | \(-0.403055\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −18.0000 | − | 31.1769i | −0.592477 | − | 1.02620i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.00000 | − | 10.3923i | 0.197279 | − | 0.341697i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −34.0000 | −1.11550 | −0.557752 | − | 0.830008i | \(-0.688336\pi\) | ||||
−0.557752 | + | 0.830008i | \(0.688336\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 45.5000 | − | 18.1865i | 1.49120 | − | 0.596040i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −7.50000 | + | 12.9904i | −0.245276 | + | 0.424831i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −6.00000 | −0.196011 | −0.0980057 | − | 0.995186i | \(-0.531246\pi\) | ||||
−0.0980057 | + | 0.995186i | \(0.531246\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 30.0000 | 0.977972 | 0.488986 | − | 0.872292i | \(-0.337367\pi\) | ||||
0.488986 | + | 0.872292i | \(0.337367\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 25.0000 | 0.814112 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 52.0000 | 1.68977 | 0.844886 | − | 0.534946i | \(-0.179668\pi\) | ||||
0.844886 | + | 0.534946i | \(0.179668\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −15.0000 | −0.486921 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −46.0000 | −1.49009 | −0.745043 | − | 0.667016i | \(-0.767571\pi\) | ||||
−0.745043 | + | 0.667016i | \(0.767571\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −8.00000 | + | 13.8564i | −0.258874 | + | 0.448383i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 57.5000 | + | 19.9186i | 1.85677 | + | 0.643205i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 33.0000 | 1.06452 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 9.00000 | − | 15.5885i | 0.289720 | − | 0.501810i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −10.5000 | − | 18.1865i | −0.337657 | − | 0.584839i | 0.646334 | − | 0.763054i | \(-0.276301\pi\) |
−0.983992 | + | 0.178215i | \(0.942968\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −3.50000 | − | 6.06218i | −0.112320 | − | 0.194545i | 0.804385 | − | 0.594108i | \(-0.202495\pi\) |
−0.916705 | + | 0.399564i | \(0.869162\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −22.5000 | − | 7.79423i | −0.721317 | − | 0.249871i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −18.0000 | −0.575871 | −0.287936 | − | 0.957650i | \(-0.592969\pi\) | ||||
−0.287936 | + | 0.957650i | \(0.592969\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −7.50000 | + | 12.9904i | −0.239701 | + | 0.415174i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −13.5000 | − | 23.3827i | −0.430583 | − | 0.745792i | 0.566340 | − | 0.824171i | \(-0.308359\pi\) |
−0.996924 | + | 0.0783795i | \(0.975025\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −3.00000 | + | 5.19615i | −0.0955879 | + | 0.165563i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −17.5000 | − | 30.3109i | −0.556468 | − | 0.963830i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 10.5000 | − | 18.1865i | 0.333543 | − | 0.577714i | −0.649660 | − | 0.760224i | \(-0.725089\pi\) |
0.983204 | + | 0.182510i | \(0.0584223\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −9.50000 | − | 16.4545i | −0.301170 | − | 0.521642i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 8.50000 | + | 14.7224i | 0.269198 | + | 0.466264i | 0.968655 | − | 0.248410i | \(-0.0799082\pi\) |
−0.699457 | + | 0.714675i | \(0.746575\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 3024.2.q.c.2881.1 | 2 | ||
3.2 | odd | 2 | 1008.2.q.d.529.1 | 2 | |||
4.3 | odd | 2 | 1512.2.q.a.1369.1 | 2 | |||
7.2 | even | 3 | 3024.2.t.e.289.1 | 2 | |||
9.4 | even | 3 | 3024.2.t.e.1873.1 | 2 | |||
9.5 | odd | 6 | 1008.2.t.a.193.1 | 2 | |||
12.11 | even | 2 | 504.2.q.b.25.1 | ✓ | 2 | ||
21.2 | odd | 6 | 1008.2.t.a.961.1 | 2 | |||
28.23 | odd | 6 | 1512.2.t.b.289.1 | 2 | |||
36.23 | even | 6 | 504.2.t.b.193.1 | yes | 2 | ||
36.31 | odd | 6 | 1512.2.t.b.361.1 | 2 | |||
63.23 | odd | 6 | 1008.2.q.d.625.1 | 2 | |||
63.58 | even | 3 | inner | 3024.2.q.c.2305.1 | 2 | ||
84.23 | even | 6 | 504.2.t.b.457.1 | yes | 2 | ||
252.23 | even | 6 | 504.2.q.b.121.1 | yes | 2 | ||
252.247 | odd | 6 | 1512.2.q.a.793.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
504.2.q.b.25.1 | ✓ | 2 | 12.11 | even | 2 | ||
504.2.q.b.121.1 | yes | 2 | 252.23 | even | 6 | ||
504.2.t.b.193.1 | yes | 2 | 36.23 | even | 6 | ||
504.2.t.b.457.1 | yes | 2 | 84.23 | even | 6 | ||
1008.2.q.d.529.1 | 2 | 3.2 | odd | 2 | |||
1008.2.q.d.625.1 | 2 | 63.23 | odd | 6 | |||
1008.2.t.a.193.1 | 2 | 9.5 | odd | 6 | |||
1008.2.t.a.961.1 | 2 | 21.2 | odd | 6 | |||
1512.2.q.a.793.1 | 2 | 252.247 | odd | 6 | |||
1512.2.q.a.1369.1 | 2 | 4.3 | odd | 2 | |||
1512.2.t.b.289.1 | 2 | 28.23 | odd | 6 | |||
1512.2.t.b.361.1 | 2 | 36.31 | odd | 6 | |||
3024.2.q.c.2305.1 | 2 | 63.58 | even | 3 | inner | ||
3024.2.q.c.2881.1 | 2 | 1.1 | even | 1 | trivial | ||
3024.2.t.e.289.1 | 2 | 7.2 | even | 3 | |||
3024.2.t.e.1873.1 | 2 | 9.4 | even | 3 |